Projection pursuit is a technique for exploratory data analysis with emphasis on visualization. It is based on finding low-dimensional projections of multivariate data that show highly nongaussian distributions. Projection pursuit is technically very closely related to ICA.
The FastICA algorithm is a computationally highly efficient method for performing the estimation of ICA. It uses a fixed-point iteration scheme that has been found in independent experiments to be 10-100 times faster than conventional gradient descent methods for ICA. Another advantage of the FastICA algorithm is that it can be used to perform projection pursuit as well, thus providing a general-purpose data analysis method that can be used both in an exploratory fashion and for estimation of independent components (or sources). Here are some publications on the algorithm.
The FastICA package for MATLAB (versions 5 or 4) is program package with graphical user interface that implements the fixed-point algorithm for ICA. See the FastICA home page.
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